From: Alex Conley (aconley@panisse.lbl.gov)
Date: Thu Apr 17 2003 - 11:28:40 PDT
Ooops, only sent this to Rob.
---------- Forwarded message ----------
Date: Thu, 17 Apr 2003 11:27:45 -0700 (PDT)
From: Alex Conley <aconley@ajanta.lbl.gov>
To: Robert A. Knop Jr. <robert.a.knop@vanderbilt.edu>
Subject: Re: further thougths on CMB vs. Helio redshifts
I should point out that you need to make sure you are doing your
K-corrections in the right way (energy) to make use of the formula with
two (1+z) factors. If you do photon K-corrections in the style of Nugent,
Kim and Perlmutter (http://panisse.lbl.gov/~nugent/papers/kcorr.ps) you
should only have one 'external' factor of 1+z (a la the d_L expression in
footnote 14 of the 7 SNe paper).
God K-corrections are confusing. I had to get reassurance from Peter
last night that the K-correction code I borrowed from him wasn't double
counting a (1+z). The answer is that if you use a d_L with only one
1+z it all works out correctly.
Alex
On Tue, 15 Apr 2003, Robert A. Knop Jr. wrote:
> >From Kolb & Turner p. 41:
>
>
> d_L^2 = R^2(t_0) r_1^2 (1+z)^2
>
> where R(t_0) is the scale factor at the time of detection, r_1 is the
> coordinate distance to the object, and z is the redshift. In this case,
> r_1 can be figured out as r_1(z). Equivalently, work out the proper
> distance to the object at time of detection, and that is R(t_0)r_1(z) ;
> this gives us (most of) our standard luminosity distance integral
> (missing one factor of (1_z)).
>
> r_1(z) should clearly just use that z that comes from cosmological
> redshift, since this is giving you the radius of the sphere surrounding
> the emitting object, and as such you want the real distance.
>
> The other z, in the (1+z)^2 above, however, should use your observed
> (geocentric) redshift, as those terms are to take care of (1) the
> redshifting of the photons (and corresponding energy loss) and (2) time
> dilation. Energy loss and time dilation will happen if it's a doppler
> shift or a cosmological redshift, so the total redshift is appropriate
> here.
>
> Probably what this means is that to do it *right*, we need to use *both*
> heliocentric and CMB-based redshifts, putting the right one in the right
> place.
>
> Does anybody agree with this, or can anybody point out a flaw in my
> reasoning?
>
> -Rob
>
>
This archive was generated by hypermail 2.1.4 : Thu Apr 17 2003 - 11:28:41 PDT